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Theorem equvini 1927
 Description: A variable introduction law for equality. Lemma 15 of [Monk2] p. 109, however we do not require to be distinct from and (making the proof longer). (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
equvini

Proof of Theorem equvini
StepHypRef Expression
1 equcomi 1646 . . . . . 6
21alimi 1546 . . . . 5
3 a9e 1891 . . . . 5
42, 3jctir 524 . . . 4
54a1d 22 . . 3
6 19.29 1583 . . 3
75, 6syl6 29 . 2
8 a9e 1891 . . . . . 6
91eximi 1563 . . . . . 6
108, 9ax-mp 8 . . . . 5
1110a1ii 24 . . . 4
1211anc2ri 541 . . 3
13 19.29r 1584 . . 3
1412, 13syl6 29 . 2
15 ioran 476 . . 3
16 nfeqf 1898 . . . 4
17 ax-8 1643 . . . . . 6
1817anc2li 540 . . . . 5
1918equcoms 1651 . . . 4
2016, 19spimed 1917 . . 3
2115, 20sylbi 187 . 2
227, 14, 21ecase3 907 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 357   wa 358  wal 1527  wex 1528 This theorem is referenced by:  equvin  1941  sbequi  1999  a12lem2  29131 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532
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